Spider-Man: No Way Home revealed Wong has taken the Ancient One's place - but he's simply assumed the role, which means he may well have failed to fulfil its mystical requirements.
According to Stephen Strange, Wong became Sorcerer Supreme during the Blip - simply because Strange himself, the other contender for the role, had been reduced to dust at the time. He's oversimplifying, probably for the sake of salvaging his own ego, because the Ancient One was killed up to a year before Thanos snapped his fingers - and choosing a new Sorcerer Supreme seemed to be a priority to defend this entire plane of existence. But it's quite possible neither truly understand what it means to be Sorcerer Supreme in the first place.
Wong may be knowledgeable, but the Ancient One kept many secrets. She served as Sorcerer Supreme for many centuries, sustained by the power of the Dark Dimension, and there's no reason to assume she kept comprehensive notes behind explaining how she took that role on in the first place. The comics may offer a crucial clue - and a recent poster may well that theory.
How Sorcerers Supreme Are Chosen In The Comics
In the comics, Sorcerers Supreme do not choose themselves - rather, they are chosen. As detailed in the Doctor Doom: Triumph & Torment graphic novel, this trio of benevolent entities are dedicated to protecting this dimensional plane from cosmic threats. Oshtur was the first of the Vishanti, an Elder God whose race ruled Earth in primeval times. Her brethren learned they could increase in power by consuming the magic of their kin, leading to a cannibalistic war that ravaged the globe; fortunately Oshtur was exploring other dimensions at the time, and she was disheartened to learn of their fate. Horrified by the actions of her fellow Elder Gods such as Chthon and Shuma-Gorath, Oshtur swore an oath not to interfere directly in Earth's affairs - but soon came to regret this vow.
The other two Vishanti are Hoggoth and Agamotto. Hoggoth was the last survivor of an ancient pantheon, who had met Oshtur during her travels and allied with her. Agamotto was her "son," and he served as the first Sorcerer Supreme. He served as Oshtur's proxy on Earth, interfering where she and Hoggoth were unable to, and he wrote a legendary tome called the Book of the Vishanti to on his knowledge to his successors. Agamotto grew in power until he ascended from this plane, becoming a principality, a higher being invoked for power. He and the rest of the Vishanti are the ones who appoint a Sorcerer Supreme - sometimes through mystical tournaments, sometimes because of an act of great heroism by which a sorcerer proves themselves the champion of an entire dimension. Oshtur blesses a Sorcerer Supreme with wisdom, Agamotto with insight, and Hoggoth with strength and power. In the comics, Strange initially became Sorcerer Supreme after battling the Elder God Shuma-Gorath; he was stripped of the role, and regained it after a tournament between Doctor Strange and Doctor Doom.
Doctor Strange 2 Could Introduce The Vishanti
Marvel has already begun setting up the Elder Gods in the MCU - with the character has a new name, Gargantos, presumably because Marvel don't own the license to Shuma-Gorath's name. This in mind, it's quite possible Marvel is blending these two monsters.
Meanwhile, there have been repeated rumors Doctor Strange 2 will introduce the Book of Vishanti - with reports it will be connected to the multiverse itself. A recent poster for Doctor Strange in the Multiverse of Madness featured a magical book in the background - and when the image was enhanced, it was clear this wasn't the Darkhold. The Cosmic Circus claim sources have confirmed this is in fact the Book of Vishanti, fitting in with these rumors - and moving one step closer to the Vishanti themselves.
Doctor Strange in the Multiverse of Madness Could Choose The New Sorcerer Supreme
It's possible the MCU will follow the same approach as the comics themselves, revealing the line of Sorcerers Supreme were established by the Vishanti. If that is the case, then Wong has assumed the title of Sorcerer Supreme simply because he believed somebody needed to possess that role - but he hasn't been officially appointed to it, because there's been no indication of a tournament and he hasn't performed any great acts of heroism to prove he has earned it. The events of Doctor Strange in the Multiverse of Madness could, therefore, be the story of how Earth's true Sorcerer Supreme is chosen.
This would perfectly parallel the comics. There, Doctor Strange proved himself worthy to be considered Sorcerer Supreme when he was plunged into a multiversal adventure; this was initiated by an interdimensional being called Nightmare, who's teased in the Doctor Strange 2 Super Bowl trailer. This ultimately led to a confrontation with Shuma-Gorath, and Doctor Strange was forced to perform an act of sacrifice to defeat him. In doing so, he proved himself worthy to become the Sorcerer Supreme, and the Vishanti recognized him as such. Doctor Strange in the Multiverse of Madness could follow exactly the same arc, culminating in the Vishanti officially declaring Strange Earth's new Sorcerer Supreme - and the vacancy left by the Ancient One's death filled at last.